Cracks in asphalt driveway
You first need to fill in the cracks. Home Depot has a variety of products available. Some are latex based that are easy to apply but probably best used for smaller cracks up to 1/2" wide. Others are cold patches that you have to compress with a tamper or by driving over them a few times. Some need to be heated with a propane torch. Those I believe are the strongest available but a little more involved. Do a search for 'asphalt patch' on the website and you'll a variety of different products.

An asphalt sealer is just a top coat. It is used to protect the asphalt from water, UV, and other things that can degrade the asphalt. Think of it like a sealer you would apply to a wood deck. It is not meant for patching. Many sealers can however fill in small cracks up to 1/8" wide. Check the labels. You'll want to reseal the driveway every couple of years or so depending on your local climate and conditions to protect it.

At my local Home Depot I see a few different sealers that are in 4 to 4.75 gallon sizes. Never seen them sell anything in stores larger than that. Those buckets they sell usually have a coverage anywhere between 300-500 square feet which is usually more than enough for an average single car driveway. You want to apply the sealer over the entire driveway because it all needs to be sealed, not just the cracks/patches. In addition to protecting your driveway it restores the color and makes it look like new.