The third definition is the one I'm using:
"1 : any of the alternative forms of a gene that may occur at a given locus"
The first two definitions seem to be a little less specific.
So, if you envision genetics as a very complex recipe on how to make a living thing you can think of each chromosome as a volume (i.e. an encyclopedia set with a separate volume/bound book for the letters A - Z). The recipe is so important that us higher animals have a two full encyclopedia sets, one from Mom and one from Dad.
In the case of alleles there are two different mutations (originally started by a copy error, probably long ago) of the same gene (think the same page in the same volume). Say for example that it turns out that a missing paragraph on page 200 of volume B is the albino mutation. What if there was a separate mutation also of page 200 of volume B? Maybe instead of the missing paragraph this one just has a misspelled word with two letters switched. Instead of making an albino this mutation might create a caramel.
If these two mutations where alleles then a homozygous albino would have two copies of volume B page 200 booth missing the paragraph creating an albino and a homozygous caramel would also have mistakes in both copies of it's volume B page 200 of but it's mistake would be different, only the two switched letters.
So if you bred a homozygous albino to a homozygous caramel neither parent would have a normal copy of volume B page 200 to give to the babies. Each baby would be a double het but since both mutations are on the same page neither baby would have a normal copy of that page and might well look part way in-between the two mutations.
So think of a locus as a certain page in a certain volume and alleles as different mistakes on the same volume and page as opposed to different mistakes on different volumes and pages. You can use this analogy further to think of linking as different mutations on different pages that happen to be in the same volume. It makes a difference because the parent tends to copy the same source volume when making a copy for it’s offspring and can only combine two linked mutations if it switches the right way between copying from it’s two source chromosomes/volumes.