Learn Danish: Vi vil rejse hjem i morgen. - We want to travel home tomorrow.

Because there is movement towards a destination. Hjem means "(towards) home", which fits perfectly with the verb rejse (to travel). If you were already resting at your house, you would use the locational form hjemme, as in: Vi er hjemme (We are at home).

Does vil mean "will" in this sentence?

No, vil is a classic "false friend" for English speakers. It usually means "want to", so Vi vil rejse means "We want to travel". If you wanted to say "We will travel" (simply stating a future fact without desire), you would normally just use the present tense: Vi rejser i morgen.

Why doesn't the verb rejse end with an "-r" here?

Because it comes right after the modal verb vil. In Danish, modal verbs are always followed by the infinitive (dictionary) form of the next verb. Therefore, we drop the present tense "-r" and use rejse instead of rejser.

Why is "tomorrow" written as two words, i morgen?

In Danish, "tomorrow" is expressed with the fixed phrase i morgen (literally "in morning"). Be careful not to confuse this with "in the morning" (referring to a time of day), which is om morgenen.