Like is pretty simple: it'a pretty much the same as "=" but with wild cards.
In your case, the most useful wildcard is probably "%" which matches zero or more of any character, much as "*" does in windows filenames.
So if you have a table contains Titles:
The Cat sat on the mat
The Cat who looked at a king
Cats a furry
The ArtistoCat
All about Dogs
Then:
SELECT Title FROM MyTable WHERE Title LIKE '%Cat%'
would return the top four titles, but not the final one.