Extracted from the website of Buddhist Vajrayana Charity Funds Association and translated (眾 生) into English:

Sentient Beings

The term ‘sentient beings’ generally refers to the beings in Realm of Delusion.
【Miscellaneous Agama Sutra雜阿含經】Fasc.6 states, “The Buddha told Radha, those who linger and are tainted by form, are called sentient beings; those who linger and are tainted by sensation, thought, volition and consciousness, are called sentient beings.” 
【Long Agama Sutra長阿含經】Fasc.22(世本緣品) records, “No hierarchy between men and women, also no difference in name, all beings who are born in this world, are hence called sentient beings.”
And according to the explanation in《Kosa Light Record俱舍論光記》Fasc.1 explains: “suffering from numerous cyclic existence (life and death), are hence called sentient beings.”
《Great Treatise on the Perfection of Wisdom大智度論》Fasc.31 and【the Mahayanabhisamaya Sutra】Fasc.1 states, “Sentient beings are temporary combination of five aggregates and synergy of conditions, hence called sentient beings.”  
【Sutra of Neither Increasing Nor Decreasing】states, “The dharma body (Dharmakaya) is tangled by troubles and worries, revolving around life and death, hence called sentient beings.” Generally, those who are concealed by the ignorance and troubles, reincarnate within cyclic existence, are sentient beings.

Buddhism states that sentient beings in the universe are uncountable and unimaginable. Other than sentient beings that exist on earth where we live, there is also the existence of sentient beings on countless planets within the universe. Other than those sentient beings whom we can see with our naked eyes, there are also many sentient beings whom we cannot see with our naked eyes. The Buddha once pointed at a glass of water on the table and said that within the one glass of water, there is the existence of 84 thousand sentient beings(in Buddha Sutra, 84 thousand means the number is innumerable)!

Even in today's scientific advancement, when one examines under the microscope, can there be less than 10 million microorganisms in a glass of water?  More than 2500 years ago, Buddha Sakyamuni, without the aid of microscope, was able to state such facts that are so scientifically correct.
How can one not be sincerely convinced (by Buddha)?

Buddhism regards all sentient beings to have limitless fortune and wisdom. On the phenomenon, each and every individual are totally different; however, from the perspective of the inner self (Buddha nature), they are completely equal.

Buddhism also considers that human life never stops and there is never any interruption, and promotes the concept of time through the following stages of life: past life, present life and future life.
Human beings go through birth, old age, sickness and death. Moreover, all materials of ‘Arising Abiding Changing Ceasing’and the world's ‘Formation Existence Deterioration Emptiness’ are the same.
However, death does not signify the extinction of human life. Human life is continuous. ‘Birth Old-age Sickness Death’ are just phenomena of human life, as the origin nature of human life is ‘Non-arising Non-ceasing’ (non-birth and non-extinction). Therefore, human life is the united embodiment of both ‘Arising Ceasing’ and ‘Non-arising Non-ceasing’; and it is the mutual interchange of all material and energy.
Thus, Buddhism has its theory of the six realms of reincarnation, being that as a lower form of life can develop into an advanced form of life, and at the same time, an advanced form of life can degenerate to a lower form of life. During this process of change, the Buddha nature does not change but exists within the storage of ‘consciousness’. Therefore, Buddhism advocates that one should perform good deeds, accumulate virtue, cultivate Buddhism diligently so as to break away from the misfortune of reincarnation.