Hi! I will try to answer your question.
These parts (U3-R-U5) form part of LTR, which are as you have said Long Terminal Repeats. Well, they are related to retrovirus and retrotransposons (in case you wanted to learn more). You can use them in a plasmid as a good promotor, especially for eukaryotic cells. Second, 5' and 3' UTR are regions inside mRNA that are no translated (this is to say that they are transcribed but not translated, so they will not form part of the protein). Finally, homology means "equal" in biology, and it is a quality. Then, it means something like they are completely identical, both left and right arm.
I hope you find it useful!
Best regards from Spain!