Translation:I live in Kyoto.
京都 (きょうと) = Kyoto, a city/prefecture in Japan
に = particle used for (among other things) marking the target location of the verb
住んでいます (すんでいます) = the polite present progressive tense for the verb 住む "to live/reside"
て-form + いる = present progressive tense; to make -む verbs into their て-form, change -む into -んで (for example: 住む 》 住んで, 飲む 》飲んで, 噛む 》 噛んで)
I might not be precise here, but ～ています adds a continuous aspect to a verb. すんでいます originates from verb すむ which means "to live". すんで is すむ transformed to a so-called "te-form" which is useful in many parts of Japanese grammar. There are some simple rules on how to transform any verb to the "te-form".
When they mean "in/at," で is used more for active actions. Like running, swimming, shopping, etc. に is used for inactive states of being. To exist somewhere, to live there. These particles have a ton of other uses that often resemble other particles, so the confusion is more than understandable!