If my mower started yesterday but won't start today even though the battery isn't dead what could be wrong with it?

From your description, you can crank the engine, so it sounds like a fuel problem.
If you left fuel in your tank over the winter, you could have water in your gas.
I would remove the spark plug, then dribble some good gas into the cylinder area; then
Put the spark plug back on and give it a crank.
If it starts briefly, then quits, you have a fuel issue.
Check your spark plug and clean or replace it if it has a lot of carbon on it.
Check for a spark by holding the spark plug wire about a 1/2 inch or less from
The top of the spark plug.

I agree with most of the post above, it does sound like a fuel problem. If you check your spark it is more of a sure thing to pull the plug, reattach the wire and let the plug rest on the block and then turn the starter. You should see a very crisp blue spark, if not replace the plug after gapping. I would drain the tank and the carvb bowl and start with fresh fuel not stored over the winter. Add a small amount of carb cleaner like SeaFoam to the fuel. You may need to spray some starting fluid into the carb air intake to get it to fire.