Basically though, in the specific example in the GP comment we know who loves whom by the order of words in the sentence - "${subject} loves ${object}" which is different from "${object} loves ${subject}". We know this because the word order in English tells us this.
But in Czech and Latin this isn't how it works - the word order doesn't have the same significance or meaning as it does in English [1]. You indicate who does what by making a little modification to the words. In this example it's one of the simpler cases - a simple verb with a subject and an object. The subject is the "nominative" case (like the dictionary/default form of a word) and the object should be in the "accusative" case. So it's actually something like "${object.nominative()} loves ${subject.accusative()}".
And just to confuse you further - it's not just "who does what" - there are other cases that denote doing something with or to or in :-) I give some examples in the above link
[1] = that's not to say word order doesn't have a role, it's just not the same role as in English
You mixed it up, it should be "${object.accusative()} loves ${subject.nominative()}".
Or, I guess, how you define "object" and "subject" for "loves" :P But grammatically, for transitive verbs, "subject" is the doer of an action, "object" is the target of an action.