To go ahead means to start/begin To go on means to continue Of course there are other meanings to these phrases by themselves but this answer is for if you're comparing the two phrases.

Both of them mean "to continue"; You say "go ahead", for example, when you're giving road indications: it is used when a person is physically moving from one place to another. You can use "to go on" when talking about feelings (think about celine dion's song "my heart will go on": her heart is not physically going anywhere, but she will 'go on', she will continue her life)