Conceptually, the verb tense of the sub-clause what the word, ‘love’ means / meant is the same as, for example, He told me his name is / was Mr Smith, so you'll often see the usage described as backshifting of reported speech - but it can apply in other contexts besides reported speech.
I should point out first of all that the "subject" of the clause (the word, ‘love’) is singular, so the Present Tense verb form must be means, not mean.
Whether to use Present Tense means or Past Tense meant is to some extent a stylistic choice, but usually we do "backshift" the verb in the sub-clause, to match the Past Tense verb in the main clause (OP's Did I know, and He told me in my example above).
You'll sometimes hear people saying that you should use Present Tense if the sub-clause refers to something that is still true (if I knew what 'love' meant before, I still do; if his name was Smith, it still is). But that can be a bit misleading. It would be more accurate to say you shouldn't use Present Tense if the subclause refers to something that's no longer true. Consider...
When I saw him yesterday...
1: ...he told me he is upset
2: ...he told me he was upset
3: ...he told me he is hungry
4: ...he told me he was hungry
Most native speakers would almost always use the Past Tense versions #2 and #4, but it certainly wouldn't always be "wrong" to use Present Tense in #1 - a "careful" speaker might deliberately do this to emphasise the fact that the person being spoken of is still upset.
We could in principle contrive a somewhat metaphorical context where hungry meant something like hungry for power, in which case even my example #3 could be validly used. But I will admit that one is rather unlikely - taken at face value, most people wouldn't accept #3 as valid.
In short, you won't go far wrong if you always backshift in constructions like this, but you shouldn't assume this is an absolute rule.