My toaster will not turn off. I press the toast button, it does it's job and then pops up, but the heating elements will continue to stay on.

It is a 'pop up toaster'. It should turn off the heat rather than 'reducing' it and pop up. The reviews mention the same. Time for a new one.

https://www.google.com/search?q=russell+hobbs+RHT302+burn+toast

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Since you don't mention the make or model number of the toaster or its age I can only make the following guesses.
It might be an electronic model. To test if this is the case, leave the toaster unplugged and push the lever of the toaster down. If it does not stay down it is an electronic toaster. If it stays down then it is NOT electronic.
The lights might be lighted push buttons.
If you plug the toaster in then put a slice of bread or two in and push the lever handle down and one light comes on then this is probably a dual purpose pushbutton. It indicates that the heating elements are on and if you push it will cancel the toasting cycle and the bread slices should pop up.
If there is a button beside the above button it could be for extending the toaster cycle time a bit longer to compensate for a thicker slice or a denser bread like a bagel. If you push it, it will light up to let you know that the cycle has been extended for this reason.
If there is a button beside this one, it could be for extending the toasting cycle to compensate for a frozen slice of bread or whatever, like a bagel or even a frozen waffle.
If you find the make and model for your toaster, it might be on the bottom somewhere, google it to see if you can download an instruction manual for it.
Hope this helps. Good Luck.

How to Fix a Broken Toaster - For Dummies

www.dummies.com/how-to/content/how-to-fix-a-broken-toaster.html

Toasters are uncomplicated appliances with heating elements, a thermostat, switches, and plugs and cords. ... If you get a shock when you touch the toaster, it's not grounded. ... What to do when your toast won't stay down ... Take off the carriagelever and front cover and look for a knob, screw, or nut located near the toast ...

How I fixed my toaster - YouTube

? 6:15
https://www.youtube.com/watch?v=QKiJkpuHy-Q
Feb 5, 2010 - Uploaded by paisteboy
Hey I know its been like 5 years since you posted this but how didyou get off the black knobs? I have a similar ... Thanks much - I shall try this on my mother-in-law's Oster toaster! ... But now that side won't stay down, so what to do? .... About · Press · Copyright · Creators · Advertise · Developers · +YouTube.

You definitely don't have the "bagel" button pressed, right? If it is in bagel mode, it only uses the heating elements on one side.

Each bay has 3 buttons: Left button: Frozen items (Waffles, etc.)
Center button: Bagel setting ( turns off the outside elements, toasting only the insides of the bagel)
Right button: Cancel (turns off the Frozen and/or the Bagel settings and "pops up" the toast.

Hola tienes que desarmarlo quiz?s se movi? de d?nde ten?a que estar y por eso no funciona

turn heat control up

I have no experience with the deLonghi toaster but in my experience automatic toaster all work in similar ways since they went electronic - toasters were about the first to do that.

Pressing the lever down against the spring pressure also presses an internal switch that sends current to the heating element as well as to the electronics that control an electromagnet, the purpose of which is to keep the mechanism engaged until the toast is brown enough and then the current to the magnet will be cut by the browning brain and the toast pops up.

If removing any crumbs from inside by inverting it and giving it a good shake and then pressing the lever a few times fairly vigorously doesn't make it work then nothing short of surgery will make it work so returning it will be the only realistic option.

You either have a stuck/defective bagel button, which turns off two elements; the elements have a break in them; or there is a wire broke or loose on the inside elements.

If you can use a multimeter, you can unplug the toaster and remove the case and check for all of these conditions. At each end of the toasting element, check for continuity, if OK, then check the bagel button to see if it is working correctly, again with the continuity check.

Check all connections to make sure none have burned off at the wire/connector points, and finally, check the thermal fuse to see if it might have failed.

Other than that, there isn't much else to check.

Hope you found this Very Helpful - Best regards!

if you mean the toast itself doesn't toast on one side, check that both heating elements have about the same resistance value. One could be twice as conductive as the other and not heat as much as the other side.
If you mean the other two slots don't toast, the problem could be in the switch or in the elements themselves. check carefully the continuity of the toaster across the (unplugged) ac power connector while you push the toaster load handle down on each side. If the resistance is significantly larger on the problem side, the problem is either the switch or the elements. The problem is usually with the switch becoming corroded or oxidized. The switch is supposed to be self-cleaning, that is, it wipes itself as contact is made to help remove buildup. Sandpaper both contacts until they shine copper colored. Otherwise look at the elements while toasting. dark areas mean lower wattage is being dissipated and the element may be bad near a dark spot.