The effects of deforestation are related with the the functions of trees.
1) Trees take up carbon dioxide from the atmosphere and release oxygen during photosynthesis. So when forests are cut down, much of the stored carbon in released into the atmosphere again as CO2 and this contribute to global warming.
2) Another effect is soil erosion: soil can be loose, it can be washed away by rain or blown away by wind if it isn't properly anchored. The roots of plants anchor the soil and if humans clear large forests, soil erosion can become a serious problem.
3) Water cycle disruption: trees and plants extract groundwater and release it into the atmosphere during the photosynthesis. So when forests are cleared, fertile soil became barren and dry. This is called desertification.