Coming from the verb 責（せ）める, meaning to have the ‘onus to do (A)’. せめて is a 副詞（ふくし） (adverb) that indicates that doing (A) is the minimum expected in order to achieve some desired outcome. It is often translated simply as ‘at least’ in English.
せめて usually alters the meaning of an entire phrase, and will appear at the beginning of sentences.

• ご飯（はん）は残（のこ）しても良（い）いから、せめて刺身（さしみ）だけは全部（ぜんぶ）たべて。
  You can leave the rice, but at least finish the sashimi please.
• せめて国語（こくご）の宿題（しゅくだい）はやっておきなさい。
  At least finish your Japanese homework in advance.

Stemming from 責（せ）める, this structure usually implies that there is some sort of onus or responsibility to do (A), rather than (A) simply being a minimum amount. Due to this, it is often used with grammar points that express desire or opinions such as たい, ほしい, てほしい, べき, and others.

• せめてこの曲（きょく）だけでも弾（ひ）けるようになりたい。
  I want to be able to play this song, at least.
• えっ... たったの5千円（せんえん）だけ？せめて1万（まん）は欲（ほ）しいよ。
  What…only 5 thousand yen? I want at least 10 thousand yen.
• 別（べつ）に毎日（まいにち）洗濯（せんたく）をしろっては言（い）わないけど、せめて晩御飯（ばんごはん）だけは毎日（まいにち）作（つく）ってほしい。
  I’m not telling you to do laundry everyday, but I want you to at least make dinner every night.
• 1日（にち）にせめて1リットルの水（みず）を飲（の）むべきだ。
  You should drink at least 1 liter of water a day.