In Russian, деятельная любовь (deyatelnaya lyubov), "active love" (our translation), is love that acts, in contrast to любовь мечтательная (lyubov mechtatelnaya), "dreamy love". Zosima gives it as the answer to Madame Khokhlakova, who asks for proof of the future life: conviction comes from the experience of this love, which is work and perseverance, whereas the dreamed kind wants an audience. The narrator says afterwards that Alyosha's love is always active.
Where It Appears
Quotes
Dreamy love craves a quick deed, soon satisfied, and for everyone to look at it. One even gives one's life, provided it does not last long, is accomplished at once, as on a stage, and everyone looks on and praises. Active love, on the contrary, is work and perseverance, and for some, perhaps, a whole science.
Book II: An untimely meeting, Elder Zosima to Madame Khokhlakova