What is the reason for tax reliefs and tax allowances?

because if every 拢 were taxed at a flat rate without allowances a greater burden would fall upon low income earners. Anyway trying to tax every 拢 of income would be futile so they give you a blanket exemption. It is the other side of the coin from an insurance company having excesses on policies so they don't have to waste time dealing with trifling claims.
Apart from that it is a small token in the redistribution of wealth mechanism.

To help people who are in a more disadvantaged situation such as people with kids who have more expenses, or someone who spends more time at work than at home on the move in a car.

our economy is driven by supply and demand
demand is how much people are willing to pay for a good at a certain time
supply is how much a supplier is willing to produce for a SPECIFIC PRICE (<--important) at a given time.

tax reliefs and allowences allow companies to produce more of a good for a lower price.

many economist believe our economy to be supply driven. because the more the supply the more people will eventually buy the more the economy grows.

the government is taking a loss in tax revenue for a growth in market.

and by the way the top 10% of money makers in the contry pay 89% of the taxes. taxing middle income people is not where the government makes it's money
Hope this helps you! PEACE

To prove extra incentives to work, to manufacture and so on.