at the back of the packet it states, "when seedlings have 3 leaves,
thin to stand 2 inches apart". the term "thin"...does that mean that i
have to slowly pull the seedlings from the earth and then transplant
them to another part?

This means that you should reduce the number of plants to maintain a minimum
distance between the remaining plants. If you fail to maintain a minimum
distance, then you will end up with stunted roots (carrots).

then the instructions continued,"plant every 3 weeks until two months
before the season's end." what does this mean? does it mean that i
divide the seeds into three ways and grow each part every three weeks?
or something else?

All of the seeds that you plant at a given time will be ready for harvest at
about the same time. If you want a continuous harvest throughout the
season, plant a new set of seeds every few weeks. You stop two months
before the season's end (usually the first frost), because seeds that you
plant after that date won't have time to make it to maturity.

can i grow them in containers?

You could possibly grow a limited number of carrots in a deep enough
container, but you'll probably get better results in the ground. Make sure
your soil is well tilled as carrots don't do well in hard compacted soil.