As a student, I wasalways confused in various Capability Maturity Models.

Based on my practical knowledge, organizational experience & knowledge gained through various sources of information, I will try to explain the 5 different CMM levels.
As we are moving up in the level, we can see effective & efficient software development processes. The reason being with each level the organization learns something new. For eg: from an ad-hoc process to a well defined process, from measuring an individual's performance to setting up metrices for measuring of management

LEVEL 1 - Ad-Hoc

This level shows inconsistency in performance. The tasks are not performed in the same way by different people. Individual's knowledge & expertise is of prime importance in L1 organizations. Here management manages people, they establishes goals for individuals & the team without concerning about how the goals will be achieved.
These are mostly schedule driven. There are no standards to measure an individual's performance, so it is highly dependent on feedbac from various stakeholders. This normally creates a politically inclined environment.

In order to move from L1 to L2 the work process needs to be defined, get the people trained & assure compliance to those work processes.

LEVEL 2 - Control

A defined process will be followed, this helps in reducing variability & a relatively constant output will be achieved.
These processes are defined without considering the minimal skills needed & impact on other processes.
Management can use theses processes & using various techniques can check the compliance to defined processes. These results can then be compared to a set of predefined results to measure people's performance.

In order to move from L2 to L3 the organization will need to build & define the core competencies.

LEVEL 3 - Core Competency

At this level the organization identifies its core competencies & then re-engineer the processes defined at level 2 to perform these competencies efficiently & effectively. It will then identify the skills required to perform those processes & staff will be recruited with the required skillset.

In order to move from L3 to L4 the organization should be able to measure quantitatively the performance of an individual.

LEVEL 4 - Predictable

At this level the organization develops the quantitative standards of work processes defined in L3 & sufficient skills are required in managers to measure manage quantitatively. This results in a predictable work process. Knowing the normal performance of the work process, management can easily measure the problems through quantitative measurements & keep projects on schedule & budget. This level of predictability uses measurement to manage as against measurement of individual's performance.

In order to move from L4 to L5 the organization is required to innovate new processes, based on available technologies.

LEVEL 5 - Innovative

The organization aspires to be a true leader in industry & always try to measure itself against industry standards & define innovative ways ti achieve higher levels of performance. This level requires constant innovation which gradually leads to constant learning both in an individual & in an organization.

From a tester's perspective : an organization with lower maturity level will tend to deliver a lower quality of software & hence bigger challenge.