Why is there a plus sign before certain phone numbers?

The + sign indicates the international codes. Thus instead of 0091... being international code for India and 001... for the US and Canada, +91 and +1 are on the mobile. If my number is 9878472630 then the std code is 09878472630 and ISD is 00919878472630 on landline phones and +919878472630 on mobiles. Please feel free to ask more if not understood.

The + signals to dial your international access code.
These are the digits that signify that a country code (rather than area code) follows.
On a mobile phone you can actually dial the + and the phone system will sort out the right code.
Another explanation

The plus sign (+) is a shorthand code for the International Exit Code when dialing an international number. So for example, depending on the country you are in, you would dial the exit code for your countr (replacing the plus sign) and then the country code, area code and local number. For example, if the number was a number in the Netherlands +44 18 9342 1011 and you were dialing from the US, you would dial: 011-44-18-9342-1011 where:

011 = US exit code (saying use international lines)
44 = Country Code (call the Netherlands)
18 = "Area Code"
9342-1011 = Local Number

If the number shows up with on your cell with a plus sign, it just means it was an international (overseas) call.