How was the writer of "The Passionate Shepherd to his love" influenced by the period in which he wrote?
Actually, the writer of this poem was a male - Christopher Marlowe, so I have edited your question accordingly. In discussing the influence of the period in which Marlowe wrote, it is important to realise how this poem fits in to the literary tradition of the time. This poem is actually part of two literary traditions - it is a pastoral poem and it is also part of the carpe diem tradition.
Pastoral comes from the Latin word pastor, meaning "shepherd". Pastoral poems are set in an idealised countryside inhabited by handsome shepherds and beautiful young women who live in harmony with nature. These pastoral poems have an elegance and an artificiality that do not really correspond to their uncomplicated characters and settings. Many pastorals express a longing for a simpler past.
Carpe diem poems (the translation is "seize the day") refer to poems that urge the reader to live life to the fullest in the here and now and not wait around (normally to fall in love).
This poem therefore can be seen to be influenced by the period in the two kinds of poem that it embodies - it is considered one of the most famous examples of a pastoral poem.