Lot of people has this understanding that Yoga and Meditation is a religious thing towards Hinduism. Even though these are originated mainly practiced by sadhus/gurus of this religion however, both Yoga and Meditation has nothing to do with Hinduism. When practiced properly they can be great benefit both for the body, mind and spirituality whichever religion one follows.
Yoga:
Yoga has tremendous potential for better health and mind. Even though it is originated in Indian subcontinent it is now practiced almost in lot of cultures and religions across the globe. Do not construe this as me pushing Hindu idealistic approach on to other religions. Even though I do not go into details of various asanas or pranayas basically when these exercises are done every muscle group of the body gets activated and blood flows into these regions thus healing the body. Also it relaxes the muscles tremendously and to a certain extent calms your mind. They help in increase in stamina and to a certain extent strength. Also on observation lot of our muscles are not stretched which can lead to cramps in the body, stooping, muscle straining etc. One can clearly see the results of yoga within couple of months of practicing.
Meditation:
The primary principal of meditation is to cease the duality of nature and bring it to singularity. What i mean is if freely allows the mind to wander, it thinks about both positive and negative aspects of life, good and bad things, pain and pleasure, etc which eventually leads to lose of focus. By practicing meditation one can eliminate these aspects and bring it to complete standstill where the person instead of thinking of being a creator of thoughts or actions becomes more of observer. At this juncture a person is not affected with duality of nature and in this state he/she becomes very calm and stable. To a large extent it is observed that religious people realize spirituality and working people realize the perfection in their fields.
Mediatation can be achevied in various forms, in spiritual world lot of religious people like hermits, sufis, popes, sadhus, etc they either practise prayers with complete devotion where as atheist people can achive the same thing by either through concentrated labour or sitting idle and concentrating on the breathing. It is very observable fact that when one works on a particular labour like swimming, fixing a bike, solving puzzle, etc often one realizes that our breathing stops for few seconds when every are extremely focus and we completely lose focus of our surroundings or people around us. And one can clearly observe during that time thoughts just appear in our mind making us feel that we are just the receptor of the thoughts to perform the action instead of actually doing the performance of thought/act.
This is the same principle with observing the breathing technique by closing eyes and sitting in the upright position. One can perform whatever religion one belongs or whether they are atheistic. Needless to say these has various benefits like stress relivar, improved focus, contentment with ones state, calm and composure of the mind, etc. This article will not go through the scientifically proven benefits of mediation however, it is left to the readers to research and find on their own.