The word Shaheed (ਸ਼ਹੀਦ) is the equivalent of the word martyr. The word has Persian and Arabic origins. A martyr is usually described as a person who suffers and endures death on behalf of a belief or faith.
Guru Arjan Dev ji was the first Sikh Shaheed. In the Sikh religion, Shaheeds are some of the most respected people after the Gurus, Bhagats, etc. Sikhism has a had a great load of Shaheeds in its history.
Guru Tegh Bahadar's shaheedi is respected by many culturals as he sacrificed his life to bring a turning point in history and a stop to the forced conversion of non-muslims to Islam by the Mughal regime.
Bhai Kahn Singh Nabha in his Mahan Kosh defines the word Shaheed as:
ਸ਼ਹੀਦ - shahīdha - शहीदਅ਼. [شہید] ਵਿ- ਸ਼ਹਾਦਤ ਦੇਣ ਵਾਲਾ. ਗਵਾਹ. ਸਾਕ੍ਸ਼ੀ (ਸਾਖੀ). ੨. ਸੰਗ੍ਯਾ- ਅਜੇਹਾ ਕੰਮ ਕਰਨ ਵਾਲਾ ਜਿਸ ਦੀ ਲੋਕ ਸਾਖੀ ਦੇਣ। ੩. ਧਰਮਯੁੱਧ ਵਿੱਚ ਜਿਸ ਨੇ ਜੀਵਨ ਅਰਪਿਆ ਹੈ। ੪. ਵਿ- ਸ਼ਹੀਦਾਂ ਦੀ ਮਿਸਲ ਦਾ. ਦੇਖੋ, ਸ਼ਹੀਦਾਂ ਦੀ ਮਿਸਲ.
This means that a Shaheed is one that gives their life for a cause that people may learn from.
The term Shaheed itself was one that was alien to the South Asian subcontinent. It was the Sikhs who claimed the word for their own martyrs and through time with various literature started to own the actual word. In this way, the Sikhs introduced this word to the subcontinent. Based on this philosophy, the concept of Shaheedi (martyrdom) for Sikhs is actually different than those for other faiths.
ਪੀਰ ਪੈਕਾਮਰ ਸਾਲਕ ਸਾਦਕ ਸੁਹਦੇ ਅਉਰੁ ਸਹੀਦ ॥
peer paikaamar saalak saadhak suhadhae aour seheedh ||
The Pirs, the Prophets, the spiritual teachers, the faithful, the innocents and the martyrs,
ਸੇਖ ਮਸਾਇਕ ਕਾਜੀ ਮੁਲਾ ਦਰਿ ਦਰਵੇਸ ਰਸੀਦ ॥
saekh masaaeik kaajee mulaa dhar dharavaes raseedh ||
the Shaikhs, the mystics, the Qazis, the Mullahs and the Dervishes at His Door
ਬਰਕਤਿ ਤਿਨ ਕਉ ਅਗਲੀ ਪੜਦੇ ਰਹਨਿ ਦਰੂਦ ॥3॥
barakath thin ko agalee parradhae rehan dharoodh ||3||
-they are blessed all the more as they continue reading their prayers in praise to Him. ||3||
Here the world Shaheed is used in that different context.