The accent shows how to pronounce it. Lava by itself would naturally be prounced with accent on the first a (or really, next to last -"penultimate"), but when you add -te, it shifts to the second a, still next to last, which is you you distinguish the singular imperative "wash yourself" with the "vosotros" (in Spain) form without the reflexive particle, as in Vosotras lavate la ropa".
The conjugation of vos has nothing to do with the conjugation of vosotros.
Vos is used in stead of tú (2nd person singular) in certain countries in America, mainly Argentina.
Vosotros (not vuestros, which is the possesive pronoun) is the informal 2nd person plural, and it is used in Spain. In America is not used as they always use the formal one (ustedes) in every situation. They have kept the formal/informal distinction in the singular though (tú/usted).
In the word "Lava" the stress falls on the next to last syllable, so according to the spanish rules of accentuation it has no written accent. In the word "Lávate" (imperative 2nd person singular) the stress falls on the 3rd to last (or first) syllable in a word with 3 syllables so due to accentuation rules it has a marked accent.
The imperative for the 2nd person singular of the verb lavar is always lávate.
Lavate (with no written accent and stressed in the next to last syllable) is not used in Spanish unless you are speaking in the voseo dialect.
The Latin-based imperative form originally only existed for tú and vosotros, since giving commands only makes sense for people you're directly addressing. At some point the honorific "vuestra merced" ("your mercy") devolved into the direct addressings usted and ustedes, but those still kept the 3rd-person grammar of the original term.
In lieu of proper 3rd-person imperative forms to give commands to your mercies, the (more polite) subjunctive got chosen instead. You can interpret the use of the present subjunctive form (like haga from hacer) as a short form of something like "Quiero que haga algo" - "I want you to do something."
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