These are the three primary types of life cycles for multicellular sexually reproducing organisms.
The diploid life cycle is the most familiar to us, because it is how animals function. The primary state of the organism is multicellular and diploid. When the time for reproduction comes around, specialized cells called gametes are produced via meiosis. The gametes are haploid. During reproduction, two haploid gametes from different organisms fuse to form a diploid zygote. The zygote then undergoes mitosis to create a multicellular diploid organism to start the cycle anew.
The haploid life cycle of organisms like fungi is spent primarily in a multicellular haploid state, where chromosomes are unpaired. Here the cells of the primary structure of the organism are haploid. During reproduction, specialized structures form to sexually reproduce by fusion of cytoplasm and nuclei, forming a diploid zygote. The zygote then undergoes meiosis to form spores, returning to a haploid state. The spores then may germinate to form the multicellular haploid organism, beginning the cycle again. Note, there is the possibility of asexual reproduction if the sexual structures of an organism fuse with cells from the same organism.
Alternation of generation refers to many plants. Here, the time spent as a diploid and haploid creature are a bit more balanced. Let's suppose we're starting in the cycle at a mature multicellular diploid point, where the organism may be called a sporophyte. Specialized cells on the sporophyte will undergo meiosis to produce spores. Spores then germinate and undergo mitosis to produce a still-haploid gametophyte. The gametophyte then produces sperm or eggs, which then combines with its complement on another organism to produce a zygote. The zygote then undergoes mitosis to form the sporophyte again.
The key with all these cycles is understanding where cells fuse and where cells undergo meiosis. The cells fuse to produce a diploid organism. Cells undergo meiosis to produce a haploid organism. If you can group the terms around what side of the haploid/diploid line they're on, then this might make the most sense.