What does "1PieceConcept" mean?

Your baggage allowance is usually determined by either 'Piece Concept' or 'Weight Concept'.

A 'Weight Concept' means you will be allowed to check-in X kg of weight. It doesn't matter how many bags there are as long as the weight of all of the bags does not exceed X kg. Some airlines will have an upper limit; like not more than 10 bags.

The 'Piece Concept' on the other hand usually refers to the number of bags that are allowed for check-in. This rules usually defines how many bags you can check-in and the weight and dimension limits of each bag as well. Since you mentioned Lufthansa you can refer to the below description for both cases.

Checked baggage – Weight Concept

First Class | Business Class | Economy Class

40 kg (88 lbs) | 30 kg (66 lbs) | 20 kg (44 lbs)

These weight limits apply worldwide except on routes on which the Piece Concept detailed below applies. Maximum baggage item weight 32 kg (70 lbs).

Checked baggage – Piece Concept

Business Class 2 baggage items of 32 kg (70 lbs) each Economy Class 2 baggage items of 23 kg (50 lbs) each

Maximum baggage item weight 32 kg (70 lbs).

LINK

Some practical examples can be: Weight Concept:

• First class traveler having just 1 32Kg bag.
• Economy traveler having 2 5kg and 1 10Kg bags.

Piece Concept:

• Economy traveler having 1 bag of 23Kg and 1 bag of 23Kg.
• Economy traveler having just 1 bag of 32Kg.

Of course, it is in human nature to maximize the benefit of baggage allowance though. :p