I am trying to understand what the phrase "eye for an eye, a tooth for a tooth" means, and I just dont get it. Can someone please explain this to me in a way that I can understand it better?

A more correct translation from the original Hebrew is: "an eye in place of/or "because of" (in Hebrew: tachat, literally: underneath) an eye…", "tachat" that it is something in place of something else, or its equivalent because of the damage (i.e. monetary equivalent to offset the injury). It means that the wounder must pay the victim exactly fair monetary damages "because" he hurt him (see Dvarim 22, 28-29, tachat, literally beneath or because of). For example, if the aggressor hurt or damaged the victim's eye, tooth or whatever, that's the amount he must pay him, e.g. the worth of an eye, because he injured the victim's eye, etc.. The amount is complexly computed exactly, including: the present as well as the future loss of the victim's job or lessening of his livelihood; the medical costs including doctors, medicine, therapy etc.; the physical pain suffered in present & future; the embarrassment of the injury & appearing crippled etc. Your common question is often asked by those who aren't familiar with the Oral Tradition and/or sometimes even anti-Semitic readers who mistakenly thought that in ancient Israel, we used to cruelly gouge out an aggressor's eye as punishment for his gouging out the eye of the victim, as was the case in some primitive ancient tribes. To the contrary, even in ancient Israel this was never the case. See Bamidbar 35, 31, where, regarding murder, the Torah says explicitly, "you shall not take monetary damages", because regarding lesser physical wounds, as in our case of the eye or tooth, the aggressor does pay monetary damages, as is clear from Shmot 21, 18-19. The Torah law takes into account the both the aforementioned exact needs of the victim- to help him deal with his new unfortunate situation, as well as the needs to punish and deter the criminal and any future possible criminals. One question still remains: If the Torah meant us to pay monetary damages, why did it write this the way it did, which may be misleading? The answer is that regular Torah studiers are aware that the Torah often words concepts in a way which is subject to several levels of understanding. The explanation offered here by Maimonides and Maharal (16th century Prague) is based upon a profound sense of responsibility for one's actions. The Torah, by expressing the payment in this way, is teaching an important and crucial lesson. Had the Torah simply ordered the aggressor to pay damages, he might have thought that it is sufficient to simply write a check to the victim and he is done. The Torah is teaching that if one perpetrates a loss of limb to his fellow, he truly deserves to have the same done to his self. He should truly contemplate the profound damage to the quality of life of his fellow, his pain and suffering he is forced to endure for the rest of his life. He has done a terrible thing and the slate will not be cleared by monetary payment alone. He must beg forgiveness from the injured party for what he has done, and perform Teshuva, repentance to God, coupled with making serious life changes that will ensure a similar act will not be repeated.