What does "This appeal comes with two heads" mean?

LGBT is essentially right.

A "head of appeal" is a reason for saying that the decision below was wrong.

Take the case of R -v- Central Valuation Officer and Secretary of State for Environment, Transport and the Regions ex. p. Edison First Power Limited (a case of which I can speak with some authority, as I was the instructing solicitor on one side). This was a judicial review challenge rather than an appeal, but the principles are exactly the same. There were two heads of challenge namely (1) the Central Valuation Officer had misunderstood, and therefore misapplied, the statutory instrument in question; and (2) if the Central Valuation Officer had not misunderstood and misapplied the statutory instrument in question, then the statutory instrument itself was ultra vires and therefore void because it created unlawful double taxation.

As you see, these two heads of challenge were mutually exclusive and, indeed, in the alternative. Success on either one would have been sufficient for the judicial review challenge to succeed. (In the event, neither was successful at first instance; the Central Valuation Officer won 3:0 in the Court of Appeal on the first head, but the Secretary of State only won 2:1 on the second head; and on appeal to the House of Lords on the second head only, the Secretary of State won 3:2)

You can have a number of "grounds of appeal" within a single "head of appeal" ... but these are not terms of art and are sometimes used pretty much interchangeably.

Probably best to think of it like this:

"We say there are three things that are wrongly decided decision below. These are our three heads of appeal. On the first head, we say there are two reasons for believing it to be wrongly decided. These are our grounds of appeal on the first head ... " and so on.

It's suitable to use if you are sure you understand its meaning and are using it correctly. It's not suitable to use if you are not.

Clarity and accuracy of thought and expression are what you should be looking for in your skeleton, not technical jargon which looks impressive but you're not quite sure what it means.