Have you travelled on a short term assignment abroad from your company? If yes, then you must have received some amount as living and housing allowances to take care of your daily expenses. Generally, your company pays you a lump sum amount on daily basis to meet your housing, living and travel needs overseas when you are travelling for short term period of about 1 - 3 months.

For example, you might receive $100 per day as a lump sum amount when you travel to USA. When you travel on short term assignments, your company keeps paying you your Indian salary in India and pays the daily allowances (called per diem) abroad in the native currency i.e. USD in our example.

What is the meaning of per diem or daily allowance?

Daily allowance or per diem is an amount which is ONLY meant to cover your daily needs of housing, travel and food. Since it is an allowance, it is NOT taxable in the country you are travelling to.
When you travel abroad for long term assignments (generally greater than 3 months), your company actually deputes you or transfers you to their subsidiary or sister company or parent company as the case may be in that country. In this case, they pay you monthly salary abroad and stop paying you your Indian salary. This salary is then taxable in the respective country.

For example, If you travel to USA for 12 months, then you may receive a yearly package of around $ 60,000 and monthy salary of $5,000. But what your take home salary will be calculated after deducting tax from $5,000.
But if you are receiving per diem allowance on short term, you would receive full $3,000 (30 days * $100) without any tax deduction.

Is per diem allowance taxable in home country i.e. India?

It is neither taxable in Indian nor abroad if it is fully spent for the purpose it has been given to you. But do remember that any unspent amount, if brought back in your home country makes it eligible for income taxes in your home country!
As per income tax rules, the amount you brought back in India should be considered as your income and added to your Indian income for calculating income tax. if you do NOT do this, it is considered as BLACK money or undeclared income.

Example: Lets assume that you received $100 per day in USA and you saved $40 per day by staying there for 30 days. When you returned back to India, you had cash worth $1200, rest $1600 was spent on your daily needs. Then this amount of $1200 would be taxable in India as per your income tax slab.

Please note that your company would normally NOT care about what you did with your daily allowance. They assume that you would have spent the full amount while your were abroad. It is your responsibility to declare the unspent amount (if any) in your Income tax return when you return back to India.

Also, note that while you were abroad and were receiving salary in India, your Indian salary would be taxable as per Indian income tax rules and your company would deduct the TDS as it used to do it when you were in India.

Is monthly salary received abroad taxable in home country i.e. India?

If you received monthly salary abroad, it is taxable as per that country's income tax laws. So, if you are in USA, you will pay income in USA and not India.

But in case, due to some trivial situation, you have been charged taxes both in India and USA the double taxation treaty may help you. India has a double taxation treaty with USA and some other countries to make sure that you do NOT pay tax twice on the same income. So, you can get the tax return if you paid taxes on certain income in both USA and India.