To expand on Edzion‘s answer, when cells replicate, they need to faithfully make an identical copy of their DNA sequence for each new cell. ‘Random genetic changes‘ are essentially copy errors of one or more bases and can occur as substitution, insertion and/or deletion of a single or multiple base(s).
Whilst copy errors occur at fairly low frequencies of about one error per ten million bases, the huge size of the human genome (3 billion bases) or even the exome (30 million bases) carries a reasonable probability that the replication process of any dividing cell would encounter one to possibly a handful of errors, but as Edzion has explained, cells contain specific proteins (MutL, MutS & MutH) that can recognise mismatch errors in the complementary strand and can fix error(s) by nicking & excising a fragment of the complementary strand containing the error and patching the gap by correctly copying the original strand, thus avoiding propagation of the error in new cells.
If the cell fails to detect or fix the error, the new cell now contains a ‘variant’ (it is now a common convention to refer to a benign variant which will not harm the organism as a ‘polymorphism‘ and pathogenic variants which will negatively impact the organism as ‘mutations’, but often the term ‘mutation’ is still applied to any genetic change, benign or harmful).
Mutations in germline cells (sperm, egg) can cause hereditary diseases, whilst mutations in somatic cells (cells other than sperm or egg) lead to dysfunctional cells, including cancer. Sometimes a single somatic mutation is sufficient to cause severe disease, but more often, a mutation in a cell will impair one of its proteins but the effects may not be evident until the cumulative effect of several different mutations, in associated proteins, over successive replications, eventually results in an affected cell which is either no longer viable (leading to necrosis and tissue damage) or very abnormal (cancer being a typical outcome). BTW, this partly explains why smoking can cause cancer at a young age (eg. a very pathogenic mutation randomly occurs in a highly significant protein) or in old age (eg. accumulation of several mutations with individually minor protein effects) and why seemingly similar cancers in different individuals behave so differently and respond very differently to different treatments (hence the value of ’personalised genomics’).
To give an example of how commonly variants occur in human germline cells, in the CFTR gene alone (underlying cystic fibrosis), which has ~189 000 bases, there are approximately two and a half thousand variants reported worldwide, of which about six hundred are considered harmful mutations causing a broad spectrum of disease severity. For CF and the many other autosomal recessive disorders, very harmful variants do propagate because only individuals who inherit harmful mutations in their paternal & maternal alleles for each particular gene are afflicted, so deleterious alleles are silently present in carriers.
Therefore, the term ‘continuously’ refers to the fact that copy errors will continue to occur, at the average frequency stated above, whenever cell & DNA replication occur, but their effects depend on whether the errors are fixed or not, and if propagated, then depends on which protein(s) is/are affected and how affected protein(s) interact.
Edited: I realised your question wasn’t posed as part of HSC exam prep, so I’ve removed a comment about the application of the term ‘mutation’ to HSC marks and also added some relevant examples of mutations on health & disease.
