Haemoglobin is what the body uses to carry oxygen in the blood.
If its high the usual cause is an underlying condition that can reduce the amount of oxygen available. For example smoking can increase your hemoglobin as can living at high altitude or chronic lung disease.

Low haemoglobin is often caused by bleeding/ blood loss. For example a menstruating woman may have low haemoglobin, someone whos had a traumatic injury with a lot of blood loss will have low haemoglobin but it may also indicate an underlying illness in someone who doesn’t have obvious source of bleeding. For example it may indicate stomach or bowel cancer as these tumours often bleed constantly but not enough that you notice but over time you are losing haemoglobin quicker than your body can make it.

Low hemoglobin can mean blood loss or some people simply run low in iron and need to take some supplements or get more iron in their diet. I run low without iron supplements.

High hemoglobin can be too much iron and people with this are often told to let their blood or donate blood to get rid of the excess iron. You can have high hemoglobin If you are very dehydrated and some heart and pulmonary issues can cause it.

Those are just some reasons.

Both can be very serious or not so serious, depends on the underlying cause and how severely low or high.

Disclaimer: I’m not a doctor.

It depends in large part on how high or low it is. High would be 15g/l or above on numerous occasions. Low would be 12 or lower on numerous occasions. The causes are varied, from polycythemia vera to lung disease to iron levels. Check it out online or tell the people to ask their doctor.

High hgb is polycythemia
Low hgb is anemia

Wow. Great answers @Lightlyseared, @JLeslie, @smudges and @Caravanfan.

Hemoglobin being low is an iron defencincy, being high is a blood disease making blood thicker than it should be, causing clots and strokes